WHC-SA-" 911-FP

Seismically Induced Loads onInternal ComponentsSubmerged in Waste StorageTanks

:- M.A. RezvaniJ. L. JulykE. O. Weiner

DatePublishedOctober 1993

To be presentedat4th Departmentof EnergyNaturalPhenomenaHazardsMitigationConferenceAtlanta,GeorgiaOctober19-22,1993

- Prepared for the U.S. Department of EnergyOffice of Environmental Restoration andWaste Management

WestinghouseP.O. Box 1970HanfordCompanyRichland, Washington99352

HanfordOperationsandEngineeringContractorfortheU.S.DepartmentofEnergyunderContractDE-AGO6-87RL10930

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DISCLM-2.CH P (t.91)

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SEISMICALLY INDUCED LOADS ON INTERNAL COMPONENTSSUBMERGED IN WASTE STORAGE TANKS

M. A. Rezvani, J. L. Julyk and E. O. WeinerWestinghouse Hanford Company

P.O. Box 1970

Richland, Washington

ABSTRACT

As new equipment is designed and analyzed to be installed in the double-shell waste

storage tanks at the Hanford Site near Richland, Washington, the equipment and thetank integrity must be evaluated. These evaluations must consider the seismicallyinduced loads, combined with other loadings. This paper addresses the hydrodynamic

- behavior and response of structural components submerged m the fluid waste.

The hydrodynamic effects induced by the horizontal component of ground shaking isexpressed as the sum of the impulsive and convective (sloshing) components. Theimpulsive component represents the effects of the fluid that may be considered tomove in synchronism with the tank wall as a rigidly attached mass. The convective

component represents the action of the fluid near the surface that experiences sloshingor rocking motion.

The added-mass concept deals with t e vibration of the structural component in aviscous fluid. The presence of the fluid gives rise to a fluid reaction force that can be

interpreted as an added-mass effect and a damping contribution to the dynamicresponse of the submerged components.

The distribution of the hydrodynamic forces on the internal components is not linear.To obtain the reactions and the stresses at the critical points, the force distribution isintegrated along the length of the equipment submerged in the fluid.

INTRODUCTION The natural frequencies and mode shapes for theconvective (sloshing) and impulsive cases are

2:his paper describes the detailed analysis used to calculated, with the added-mass effect included. Alsodetermine the dynamic response of submerged internal presented are the convective potential function and thetank components during an earthquake. In particular, corresponding fluid velocities. Stresses in the internalthe paper addresses the hydrodynamic forces on an component are calculated for hydrodynamicallyinternal component suspended in an underground waste induced loads. The stresses then are combined with

storage tank at the Hanford Site near Richland, other stresses to evaluate and qualify the componentWashington. The internal component response is against national codes and standards. For comparison,predicted for seismic loads caused by an earthquake with the maximum numerical stresses resulting from thezero period acceleration (ZPA) of 0.2 times the hydrodynamically and seismically induced loads aregravitational acceleration (0.2 g). presented.

Closed-form solutions were used to calculate the The impulsive effects were calculated to Tankconvective and impulsive effects on the submerged Seismic Experts Panel (TSEP) guidelines [1]. The

equipment, response spectra curves were taken from Hanford Site

t

design criteria, SDC-4.1 [2]. The TSEP requirement of It is expected that a pump installed in the tank, to0.5-percent damping was used for the :doshing mode. inject caustics and mix the contents, will keep theThe response spectra for 2.0-percent damping was scaled sludge suspended in the liquid waste and the contentstlp for the analysis [3]. The ZP., .ras kept at 0.2 g to homogenous. The average specific weight of the wastecomply with SDC 4.1. is 1.4.

GEOiX{ETRY AND MATERIAL APPROACH

The component under consideration is a 55-ft long, The analysis sequence and assumptions are2-in. diameter Schedule 40 pipe made of A-106, outlined in this section. The f'mal results are the forcesGrade B carbon steel (Figure 1). The pipe is secured to and stresses at the interface where the T/C treethe tank dome at the top and free at the bottom, connects to the tank dome. This connection yields the

suspended in the tank as a cantilever where the bottom maximum stresses used for evaluation and qualificationend is 1 ft from the tank bottom. Thermocouples are of the equipment.attached to the pipe to monitor the temperature of thetank contents as a function of elevation. Throughout this The hydrodynamically induced loads acting on thepaper, this equipment is referred to as the thermocouple T/C tree resulting from the horizontal component oftree (T-/C tree), the ground shaking are expresses as the sum of

convective and impulsive components.b/'__ Tr_

, _ CONVECTIVE MODES•r.,,_s_\_ ___2__"_ _ The contribution of convective (sloshing) loads are

___ r,_va_t._ obtained by expressing the motion of the fluid in terms

i i of a potential function, _.

A _ .... _. _'2"-',,,. _ ". _ ': .._.2.22.2_..' .t '_ I

_i I _z-.taq,_z_.................w,,_" _t,.rc!' The sloshing assumptions listed below are used for thef:_-:-'--'_'_'_.'--":" "-. q, ;, derivation [4].

_._t l '-'#"' _.'r::l_"" ' ; I

w,a 1 The liquid is homogeneous, inviscid, irrotational,9oo

vr and incompressible.450

• 2. The boundaries of the tank are rigid.

_,,,h 3. The wave amplitudes are sufficiently small in

comparison with the wavelengths and depths to

_" ........-._4 / permit nonlinear effects to be neglected.

co=vo,_ 4. The influence of the surrounding atmosphere isnegligible.

- .',lot,tn-so_ EartaOmm

5. The influence of surface tension is negligible.

Figure I. Schematic of the Waste Storage Tank and The fluid velocities are derived by applying

the Location of the Internal Component. response spectrum techniques in conjunction with themethodologies outlined in References [1] and [4]. The

The T/C tree is inside a 1,000,000-gal double-shell three modal velocities (radial, tangential, and vertical)waste storage tank at the Hanford Site. The tank, 75 ft then can be calculated as spatial derivatives of thein diameter and approximately 47-ft deep, is designated potential function. These modal velocities are used toas tank 241-AN-107. The tank contains radioactive obtain the actual fluid velocities by modal comSinationwaste, distributed as follows: 26 ft of liquid waste over techniques.6.5 ft of sludge; a total waste height of 32.5 ft(Figure 1). The T/C tree is located at a radius of 20 ft Next, the drag forces on the T/C tree arefrom the center of tank. calculated with standard drag formulas for flow over a

stationary cylinder. The appropriate dynamic load

i

, t

factor, DLF, also is included, g = gravitational accelerationi -- 0, 1, 2 ....... 6 number of nodal diameters

IMPULSIVE MODE j = 0, 1, 2 ....... 6 number of nodal circles.To calculate the impulsive mode contribution, TSEP

[1] guidelines provide a dimensionless function defining Selected mode shapes for 0 = 0, and r = 0 to Rthe impulsive component of the wall pressure vs. axial (37.5 ft, which is the tank wall location) are plottedposition. Then the pseudo-acceleration at the impulsive below. Only modes with i = 1 are of interest.natural frequency induced by the earthquake motion is

calculated, enabling the calculation of forces on the _.

component associated with the impulsive mode. 1]

The absolute sum of the convective and impulsive .-_., 0.5 ,___.__._ ._

forces then varies with fluid depth; the value is used for "," ',. t._ " '.the reaction and stress calculations at the critical _ 0

location, the connection of the T/C tree to the tank _Sdome. The variation is not linear; to obtain shear and ,_ --0.5 I Imoment reactions, the total force distribution is I [

integrated along the length of the equipment. Likewise, -]" 0 0.z 0._, 0.sl 0.sl 1.

the stresses (axial, bending, and shear) can be I"/Rcalculated.-'*-=ode shape ac i-L, .I,..0

_ode shape ac i-L, ].!-_)_ shape _c i-].,

ANALYSIS -_-- _ sh,p, ,= L-t.

CONVECTIVE ANALYSIS

Convective (sloshing) effects are caused by the

earthquake-induced motion of the free surface of the Figure 2. Mode Shapes as a Function of r fortank waste. 8 = 0 (note: i = 1, j = 0..013).

The mode shapes of the potential function, _j, andthe natural frequency of a tank with radius R can be _(I", 0, i, j)written [4, 5, and 6] as a function of Bessel's function,tank radius, and radial and circumferential location of O. 582interest in the tank as shown below.

_j (r,0,i,j) = Ji(liJR)COS(iO ) (1)

-0.582r 9

Figure 3. Mode Shapes as a Function of r and 0where (note: i = 1, and j = 0).

_5u - mode shape of the potential function The spectral acceleration at 0.5-percent dampingJi(X) = Bessel function of first kind [1] for the sloshing modes is determined from an

k u = ij th root of the first derivative of Bessel's extrapolation of the 0.2 g ZPA response spectrafunction of the first kind and first order, (Newmark-Hall) curves [2]. Thus, a 50-percentile

J'i(_kl.j) -- 0 acceleration scaling of the response curve at 2-percentr,0 = radial and circumferential location, polar dampira_ is applied as outlined in Reference [3]. The

coordinates resulting response spectrum is shown in Figure 4.R = tank radius = 37.5 ft

h = fluid height in the tank = 32.5 ft

fij = natural frequency of ij slosh mode.

where

I ' : : ;;_' ' ....... % i i _ i i _:,_ S,i] = Resulting spectral acceleration at 0.5) I : t . (4. : _ _,, ' _ -'

A I I i_J-_" i i J ili _ I I,

"_ J ,_S_II i ! ]l]il { [Ill[ The maximum wave amplitude, A_ij, for each-,_ 0._ _ ;'. .... convective mode shape is given by(,we)

n_,,. (6),(m_ _(r.o,/J)

0.oiO.l L '¢, lO0

Frequency (Hz)--*--0.5z Dmvtr,_ The above parameters complete the elements required2% l_a_tns

-----5x D,,=vt,,8 to scale the potential function, _(r,0,z,i,j), at themaximum response as

Figure 4. The Modified Newmark-Hall Response

O(r,0,zjj) _(r,O,ij) (7)

Next, a dimensionless function defining the axial o_ h(-_2)variation of the wall pressure associ_.ted with the ij th co_ h

sloshing modes of vibration is given by Equation 3 [1].

where

C = 2 [R ] (3) surface, Figure 1.

Cii (_.ij)2--1 cosh(-_)h w_j =circular frequency = 2"n'f_j.The velocity components then are calculated by

using the potential function. The amplitude and phaseTo calculate the maximum modal vertical angle are calculated by assuming that the component of

displacements, Equation 3 is maximized at the liquid fluid velocity normal to the side and bottom of the tanksurface (z = 0) to give is zero. The radial, circumferential, and vertical

velocities in cylindrical coordinates are calculated from

2

Cmax_"" (3._ z- 1 (4) v,(r,O,z,i,l) =-O-_-_(r,O,z,id)or

The maximum modal vertical displacements (r/_,,_),at the fluid free surface, is defined as vs(r,O,z,i,l) = 1 Ota, .. -.., (8)

1"1_ = CmuvRSog (5) vz(r,Oc.,ij) -_ _a_._ (r,O,z,ij).g

The modal combination of velocities are c,_Iculated

by the square-root-sum-of-squares (SRSS) for the ijmodal velocities.

2I

J 1.5

__ 0=_'/2

The axial distribution of v, and v0at the T/C tree radial > _ /'- =0 _

location is illustrated in Figure 5. The horizontal in- 1 '_ )_

plane resultant fluid velocity, v (r,O,z), is.

v(r,0,z.) = _/Vr(r,0,Z) 2 + v0(r,0,Z) z (10) _

The axial distribution of v (r,0,z) at the T/C tree radial 0.5location is shown in Figure 6 for selected values of O. 0 0.5 1

Ftee Bottom ofsurface -z/h Liquid

Figure 6. In-Plane Resultant Fluid Velocity at2 r = 20 ft, O=0, "n-/4,_/2, as a Function

of z.

N The drag force per unit length on the T/C tree isVa given by. /--

,,

F,_r,e,z). C_r,O,z)_,_,v(r'o'z)2• D (11)2

¢_ a.at4-

.-_ _'_ whereN

__ '__'_-k'k" Cd = Drag coefficient for a circular cylinder

as function of Reynold number along the,.. T/C tree [9]>

D = Diameter of the submerged T/C tree_ (2 in).0.5 p,.,.,. = Mass density of w_te (87.4 lb/fd).

o 0.5 i

Free -Z/h Bottom of To account for the dynamic behavior of the T/CSur#ace Liquid tree and the liquid, a dynamic load factor (DLF) is

applied to the drag force. The DLF includes thenatural frequency of the T/C tree, the sloshing forcedfrequency, and a 5-percent structural damping. The

Figure 5. Maximum In-Plane Velocity components DLF can be calculated as follows [7].as a Function of z, Radial (0=0) andCircumferential (0=r/2), at r = 20 ftCI'/C Tree Location). D/..F= I = 1.265

1[1 =(It.o]2_ (12)

p, J

where TOTAL FORCE

The total force per unit length caused by the_" = Structural damping (0.05) impulsive and convective (sloshing) effects isft.0 ---=Minimum sloshing frequency, forced

vibration (0.192 Hz) Fto_ (r,O,z) = Fl(r,0,z ) + (DLF) Fo(r,0,z ). (15)tzc = Minimum T/C tree frequency, natural

frequency with added mass in viscous fluid The total force, Ftot_ , the sloshing force, FD, and the(0.1439 Hz) [10]. impulsive force, F1, for the thermocouple location are

plotted in Figure 8, for three different 0 values, as aIMPULSIVE ANALYSIS function of z. The depth is normalized with respect to

The impulsive component of the wall pressure, Ct, the fluid depth, h.as a function of the vertical displacement of the fluid iscalculated from [1]. One can use the value of Fto,_ and integrate along

the length for shear and moment values at theconnection of the T/C tree to the tank or any otherN N

Cl(r,O,z) = 1 - _ _ Ccv. (13) location of interest. The axial, bending, and sheari.-1 /_t stresses also can be calculated. The equations are

- listed below; results at the radial !ocation of the T/C

tree for different radial angles are tabulated in Table 1The plot of Ct and Cc for 0 = 0 and r = R ft, is shown

for i = 1 and j = 0 to 6, modes of vibration.in Figure 7 as a function of axial position z (i = 1).

Shear forceI.

A ._ V(r,O) = ,,u(r,0,z)dz (16)

NN

- _ ,//

// M(r,O) = f]_(L - nrc - z)F,_r,O,z_ (17)0

o o.z o.,. o.+ o.+

-z/h Axial stress

-+- C (r,0,z)--x_ C¢(r,0,z) Oo =g---_-.mrc.L- p.,aae'g'hrc (18)

ATc

Figure 7. Convective and Impulsive Functions for

r = R, 0 = 0, and as a Function of z. Bending stress

The buoyancy force per unit length resulting from

the acceleration of fluid waste for the impulsive mode, M(r,o).D

FI, is given by ot,(r,0) _ 2 (19)Irc

Ft(r,O,z ) n := p,,,_r,_D Ct4 z . (14) Shear stress

The A, factor denotes the impulsive component of the V(r,O)

instantaneous pseudo-acceleration induced by the x(r,0) - )lrc (20)earthquake motion and refers to the fundamental

frequency of the tank vibration (7.16 Hz) including theimpulsive component of liquid mass [1 and 8].

I '

, e,

I -- 1.2 1.2

A t#.

aJ 0 8 '_

L _ ,f- 0 _ _e_Jee_,ee_ ta..o . tj.0.6 -r--------- u 0.6 , -

._ , _= . = 0 • _ 0.4--

o 02 _.." / %,_ ._ 02 "_ 02

J0 _ ' 0 c------ 0 .....................0 0.5 ! 0 0.5 ! 0 0.5 i

- -zlh -z/h -z/h

(a) (b) (c)

--w- Fto:_t(r, O,z)

--_ Fz(r,#,z)-,-- Fo(r,#,z )

Figure 8. Force Distributions Along Thermocouple Tree as a Function of z for r = 20 ft and O = 0 (a), 7r/4 (b),and 7r/2 (c), Respectively.

the thermocouple tree.where

The fundamental natural frequency of the T/C treehTc = Height of thermocouple tree submerged in (with and without the added mass), sloshing '

the fluid waste (convective mode), and tank-liquid-system (impulsive(31.5 ft) vibration mode) are 0.1439, 0.1917, 0.192, and 7.16

L = Total length of thermocouple tree (55 ft) Hz, respectively.ATC = Thermocouple tree cross-sectional area

(1.0745 in=) The analysis considers a north-south (0 degree)m-rc - = Mass of thermocouple tree pipe (4.6505 seismic earthquake with the T/C tree 20 ft from the

Ib/ft) tank center. The maximum stresses for 0, 45, and 90

ITC = Thermocouple tree moment of inertia degrees are calculated. Obviously, the maximum(0.6657 in4) numerical value occurs at 0 degrees. The effects of

D = Diameter of thermocouple tree convective and impulsive fluid-induced stresses are(2 in.). compared against the seismically induced stresses with

added mass in an atmospheric environment, Table 2.SUMMARY AND CONCLUSIONS

The analysis considers the hydrodynamic effects ofthe liquid on the T/C tree. For calculation of thedynamic behavior of the fluid on the T/C tree, thesloshing modes (i = 1 and j = 0...6) are considered tocontribute to the dynamically activated loads acting on

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Table I. Maximum Hydrodynamic Results for 0-, 45-, and 90-Degrees Location of T/C Tree with Respect to aNorth-South Earthquake Load.

....

Maximum Hydrodynamic Results 0 Degrees 45 Degt'ees 90 Degrees.....

Fluid Waste Velocity (ft/see)

1. Resultant in-plane (@ T/C) 1.8 1.9 1.92. Vertical @ tank wall, r=R 2.6 1.8 0

....

Forces on TC at Surface 0bf/ft)

1. Drag force (convective, FD) 0.76 0.81 0.86

2. Buoyancy force (impulsive, Ft) 0.74 0.52 0

3. Total hydrodynamic forge (F_,a) 1.71 1.55 1.09..... , ,, ,,,

Reaction Forces on TIC at Flange

1. Shear force (lbl) 25.3 22.6 12.8

2. Moment (in-lbl) 11,968 10,412 5,271

Stresses on TIC at Flange 0bf/in:)1. Axial stress 186.4 186.4 186.4

2. Bending stress 21,347 18,573 9,4023. Shear stress 23.6 21.0 11.9

.,

Table 2. Maximum Hydrodynamic and Seismic [4] Blevins, R. B., 1984, Formulas for NaturalStresses on the T/C Tree for a Design- Frequency and Mode Shape, Van NostrandBased Earthquake (DBE) Event Occurring Reinhold Company, New York, New York.in the North-South Direction.

[5] Abramowitz, M., and J. A. Stegun, Handbook ofMathematical Functions, Dover Publication, Inc.,

Stresses at the flange location p. 411, p. 468, (formerly published by U.S.Loading 0bf/in:) Government Printing Office, Washington, D.C.),Condition -

New York, New York.Axial Bending Shear

. [6] Lamb, H., 1945, Hydrodynamics, Sixth Edition,Hydrodynamic 186.4 21,347 24 Dover Publications, Inc., New York, New York.

Seismic .205 5,245 22 [7] Biggs, J. M., 1964, Introduction to Structural

Dynamics, McGraw-Hill Book Company,REFERENCES New York, New York.

[1] TSEP, 1993, Seismic Design and Evaluation [8] Rammerstorfer, F. G., K. Scharf, and

Guidelines for the Department of Energy High-Level F.D. Fisher, 1990, Storage Tanks underWaste Storage Tanks atm Appurtenances, Tank Earthquake Loading, Applied Mechanics Review,Seismic Experts Panel, Brookhaven National Vol. 43, No. 11.Laboratory Associated Universities, Inc.,

Upton, New York. [9] Daugherty, R. L., and J. B. Franzini, 1977, Fluid

Mechanics with Engineering Applications, seventh[2] SDC-4.1, 1989, Standard ArchitecturalCivil Edition, McGraw-Hill Book Company, New

Criteria, Design Loads Jbr Facilities, Rev. 11, York, New York.Westinghouse Hanford Company, Richland,

Washington. [10] Chen, S. S., M. W. Wambsganss, andJ. A. Jendrzejczk, 1976, Added Mass and

[3] Harris, C. M., and C. E. Charles, 1976, Shock and Damping of a Vibrating Rod in Cor_ned ViscousVibration Handbook, Second Edition, McGraw Hill Fluid, Journal of Applied Mechanics.Book Company, New York, New York.

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